PRP Records

Probable Primes Top 10000

(259919 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
9001(2^223754+658)/267357Stefano Morozzi01/2020
9002V(340138)67336Serge Batalov03/2015
900343125^14528-10667334Enzo Doria07/2012
900415275^16086-16086^1527567304Norbert Schneider09/2018
90058*10^67302-5167303Robert Price10/2017
9006(2^223551+1634)/267296Stefano Morozzi01/2020
900717458^7153+7153^1745867292Hans Havermann08/2016
900816366^12925+12925^1636667288Hans Havermann08/2016
900937^42906-267286Lelio R Paula08/2013
901018^53592-1367273Lelio R Paula08/2013
9011V(396221)67256Serge Batalov03/2015
9012(2^223401+906)/267251Stefano Morozzi01/2020
9013(2^223382+2338)/267245Stefano Morozzi01/2020
9014(34*10^67245-7)/9/3^4/193/138153767236Makoto Morimoto04/2016
9015(14*10^67235-101)/367236Robert Price04/2017
901653^38993-52^3899367235Robert Price01/2013
9017(2^223349-7)/648567231Lelio R Paula04/2012
90182^223333+31567230Lelio R Paula04/2012
9019(2^223318+574)/267226Stefano Morozzi01/2020
9020(2^223301+1590)/267220Stefano Morozzi01/2020
90212^223278-11104167214Enzo Doria05/2014
9022(2347*2^223281+1)/(3*5*197*1213*1783)67208Jens K. Andersen09/2007
90232^223256-4567207Lelio R Paula02/2012
90242^223253-11211167206Enzo Doria06/2014
902618407^4474+4474^1840767199Hans Havermann08/2016
9025(2^223228+3342)/267199Stefano Morozzi01/2020
9027(2^223206+2194)/267192Stefano Morozzi01/2020
902847^40182+40182^4767189Norbert Schneider11/2014
902913^60309+9467181Lelio R Paula07/2013
903011^64503-8467173Lelio R Paula07/2013
90313^140781+23667170Lelio R Paula06/2013
9032(2^223110+3382)/267163Stefano Morozzi01/2020
90332^223107-86505767162Paul Bourdelais03/2013
90342^223100-5967160Lelio R Paula02/2012
9035(2^223098+2394)/267159Stefano Morozzi01/2020
90362^223087+7196367156Enzo Doria04/2016
9037(2^223032+2410)/267140Stefano Morozzi01/2020
9038(2^223034+1122)/267140Stefano Morozzi01/2020
904018^53481-377967134Enzo Doria03/2013
9039(326^26713-1)/32567134Eric Chen09/2017
90414^111473-6257367114Mike Oakes02/2011
90422^222943+2967113Henri Lifchitz08/2005
9043(2^222939-9)/10367110Lelio R Paula04/2012
90442^222862-45916167089Enzo Doria05/2015
90452^222828+819367078Lelio R Paula04/2012
90463^140570+266067069Lelio R Paula06/2013
904720731^1716+1716^2073167055Hans Havermann08/2019
90482^222744+85567053Lelio R Paula04/2012
904913^60189+8467048Lelio R Paula07/2013
9050(2^222721+2034)/267046Stefano Morozzi01/2020
90512*10^67043-5167044Robert Price11/2017
905222588^929+929^2258867042Hans Havermann08/2019
90532^222701+57729457567040Lelio R Paula02/2016
9054(13*10^67038-31)/967039Serge Batalov11/2008
9055(151*10^67027-7)/967029Robert Price07/2017
9056(2^222659+1554)/267027Stefano Morozzi01/2020
9057(2^222640+3810)/267022Stefano Morozzi01/2020
9058(58695*2^222620-1)/6167019Lelio R Paula04/2015
90592^222614-11104167014Enzo Doria05/2014
906016255^13242+13242^1625567003Hans Havermann08/2019
906116477^11650+11650^1647767001Hans Havermann08/2019
9062118^32333-11766991Norbert Schneider08/2018
90632^222520-190766986Yves Minet03/2013
9064(2^222499+2694)/266979Stefano Morozzi01/2020
9065(4^111231+23)/366968Robert Price02/2017
906616206^13549+13549^1620666962Hans Havermann08/2019
90672^222408-11127566952Enzo Doria05/2014
906810^66949-9^6694966949Jean-Louis Charton12/2005
9069(2^222394+2790)/266947Stefano Morozzi01/2020
90702^222378-100566943Lelio R Paula04/2012
9071(9*2^222366+1)/7366938Lelio R Paula08/2012
90727^79202-6^(79202+1)66934Robert Price06/2016
90732^222325-11225566927Enzo Doria06/2014
9074(2^222318+1290)/266925Stefano Morozzi01/2020
907521789^1178+1178^2178966918Hans Havermann08/2019
907620^51428+3366910Lelio R Paula08/2013
9077(2^222237+2682)/266900Stefano Morozzi01/2020
90792^222224-1850966897Enzo Doria05/2013
9078(38*10^66896+187)/966897Robert Price11/2017
9080(2^222205+1826)/266891Stefano Morozzi01/2020
90812^222192-86968810566887Lelio R Paula02/2016
9082(2^222175+3206)/266882Stefano Morozzi01/2020
9083(19*10^66878-43)/366879Robert Price10/2017
908411^64219-6466878Lelio R Paula07/2013
90852^222151-1729566875Lelio R Paula04/2012
9086gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
90872^222085-11103166855Enzo Doria05/2014
90888*10^66848-1366849Robert Price05/2017
9089(3^140087+4)/1366838Lelio R Paula04/2012
9090(3^140102+4)/884360943766836Lelio R Paula04/2012
909119^52265+5266835Lelio R Paula08/2013
90922*10^66826-2766827Robert Price02/2017
9093(2^221971+3686)/266820Stefano Morozzi01/2020
90944*6^85867+566819Lelio R Paula09/2014
909511955^16384+266807Matt Stath12/2018
909615^56800+866802Lelio R Paula08/2013
9097(2^221891-2^110946+1)/56679611/2006
909810^66793+6944166794Patrick De Geest05/2013
909910^66793-6366793Robert Price05/2011
9100(2^221880+2730)/266793Stefano Morozzi01/2020
910135^43256-170466791Enzo Doria03/2013
91023^139976+2^(139976-1)66786Robert Price05/2016
910388769!6-4866786Robert Price08/2018
91047^79023-5466783Lelio R Paula06/2013
9105104^33109-10366782Norbert Schneider11/2016
9106(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
9107(2^221812+1290)/266772Stefano Morozzi01/2020
9108(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
91102^221768+18366759Lelio R Paula02/2012
9109gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
9111(154*10^66755-1)/966757Serge Batalov12/2014
911211^64097+4866751Lelio R Paula07/2013
9113(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
9114(19*10^66748+413)/966749Robert Price10/2017
9115(2^221732+2490)/266748Stefano Morozzi01/2020
9116(3*2^221696-1)/1366737Lelio R Paula01/2014
91178*6^85758-766734Lelio R Paula09/2014
9119135^31325+266733Lelio R Paula05/2013
9118(2^221682+3750)/266733Stefano Morozzi01/2020
9120(49*10^66729+41)/966730Robert Price07/2015
9121(2^221650+430)/266723Stefano Morozzi01/2020
9122(349*10^66720-7)/966722Robert Price03/2017
9123(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
9124(2^221624+2170)/266716Stefano Morozzi01/2020
9125(25*10^66714+71)/366715Robert Price01/2017
912611^64061-78066713Enzo Doria11/2012
9127(2^221590+3238)/266705Stefano Morozzi01/2020
91287^78929+466703Lelio R Paula06/2013
912911^64048-93066700Enzo Doria11/2012
9131120^32079-11966699Norbert Schneider09/2018
9130(2^221567+1418)/266699Stefano Morozzi01/2020
91322*7^78921+566697Lelio R Paula09/2014
9133(25*2^221526+1)/40966685Lelio R Paula08/2012
913416330^12117+12117^1633066682Hans Havermann08/2019
9136(2^221509-1)/29239188166673Jens K. Andersen02/2009
9135(2^221483+1218)/266673Stefano Morozzi01/2020
91372^221479+7295366672Enzo Doria04/2016
913910^66666+27540366667Patrick De Geest03/2010
913816317^12182+12182^1631766667Hans Havermann08/2019
914010^66666-11552166666Patrick De Geest03/2010
9141(18*10^66657-81)/9966657Ray Chandler01/2011
9142(2^221425+1746)/266656Stefano Morozzi01/2020
91434*10^66653+2166654Robert Price08/2016
9144(10^66650+149)/366650Serge Batalov12/2014
9145(2^221398+3654)/266648Stefano Morozzi01/2020
91469^69842+3*8^69842-2*4^69842-3*2^6984266647Mike Oakes12/2010
91472^221391-214566646Lelio R Paula04/2012
914822952^801+801^2295266645Hans Havermann08/2019
9149(2^221347+3146)/266632Stefano Morozzi01/2020
9150(5*10^66613-119)/366614Robert Price04/2016
91512^221273-11323366610Enzo Doria07/2014
9152(2^221234+2994)/266598Stefano Morozzi01/2020
91533^139571-4666593Lelio R Paula06/2013
9154(4*10^(2*33295)-2*(10^33295)+1)/366591Robert Price04/2018
91552^221181-86968810566583Lelio R Paula02/2016
9156(61*10^66575-7)/966576Ray Chandler02/2012
9157(2^221131+1850)/266567Stefano Morozzi01/2020
91582^221126+13366566Lelio R Paula02/2012
915912^61680+9166564Lelio R Paula07/2013
9160(lucasV(1,2,442258)+2)/10366564Mike Oakes04/2017
9161(2^221090+1782)/266555Stefano Morozzi01/2020
9162(13*10^66551-73)/366552Robert Price12/2016
916311^63901-159066547Enzo Doria12/2012
916411^63901-150066547Enzo Doria12/2012
91656^85517+2366546Lelio R Paula07/2013
9166(2^221047+566)/266542Stefano Morozzi01/2020
916917^54069-4066530Lelio R Paula08/2013
9167(2^110503+4725)^2+(2^110503+4725)+4166530Makoto Morimoto05/2016
9168(2^110503+8099)^2+(2^110503+8099)+4166530Makoto Morimoto05/2016
9170(2^221004+450)/266529Stefano Morozzi01/2020
9172(2^221008-1017)/7853366526Lelio R Paula04/2012
91713^139432+2666526Lelio R Paula06/2013
9173((2^110503+5139)^2+(2^110503+5139)+41)/2086579766523Makoto Morimoto05/2016
9174((2^110503+6647)^2+(2^110503+6647)+41)/197/1732766523Makoto Morimoto05/2016
91756^85481+8548166518Henri Lifchitz08/2014
9176(2^220925+3834)/266505Stefano Morozzi01/2020
9177(9179*2^220913-1)/39966503Lelio R Paula04/2015
917813^59687+6666488Lelio R Paula07/2013
9179(49*10^66485-31)/966486Robert Price07/2015
9180(2^220841+1062)/266480Stefano Morozzi01/2020
9181(2^220815+950)/266472Stefano Morozzi01/2020
9182(46*10^66469+17)/966470Robert Price06/2015
91832^220790+9766465Lelio R Paula02/2012
9184(23*2^220790+1)/80766463Lelio R Paula06/2012
918540009^14441-10266460Enzo Doria07/2012
9186(2^220766+3190)/266457Stefano Morozzi01/2020
91872^220736-14366449Lelio R Paula02/2012
918861077!4-6466448Robert Price11/2019
9189(79*10^66447-97)/9966447Ray Chandler01/2011
919021235^1344+1344^2123566432Hans Havermann08/2019
91912^220675+6966430Lelio R Paula02/2012
9192(2^220671+498)/266429Stefano Morozzi01/2020
919419049^3070+3070^1904966427Hans Havermann08/2019
9193(2^220665+974)/266427Stefano Morozzi01/2020
919688323!6-1666419Robert Price08/2018
9195(2^220637+3974)/266419Stefano Morozzi01/2020
91972^220633-11138166418Enzo Doria05/2014
9198(2^220625-509203)/400032166409Lelio R Paula05/2012
91992^220596-1581366407Enzo Doria04/2013
9200(5*10^66394-17)/366395Serge Batalov05/2009
92012^220549-185917366392Enzo Doria04/2016
9202(2^220519+3858)/266383Stefano Morozzi01/2020
9203(2^220514+1294)/266382Stefano Morozzi01/2020
9204(2^220485+3434)/266373Stefano Morozzi01/2020
92052^220478-16166371Lelio R Paula02/2012
9206(2^220470+1278)/266368Stefano Morozzi01/2020
92075^94938-1463666359Enzo Doria02/2013
9208(F(67)^4861-F(66)^4861)/F(65)66353Wayne Halsdorf03/2012
920915444^15839-15839^1544466346Norbert Schneider08/2018
92102^220253-11487166303Enzo Doria05/2015
9211(2^220244+3226)/266300Stefano Morozzi01/2020
921212^61432+9566297Lelio R Paula07/2013
92132^220192-11156366285Enzo Doria05/2014
92142^220188-11144966284Enzo Doria05/2014
9215(4*10^66284+23)/966284Robert Price11/2014
9216(2^220155+1626)/266273Stefano Morozzi01/2020
9217(2^220150+2950)/266272Stefano Morozzi01/2020
921832501!2+266266Robert Price01/2015
9219(8*10^66261-101)/366262Robert Price10/2017
92201530*10^66254+R(66254)66258Patrick De Geest05/2016
9221(47^39623-1)/4666252Robert Price06/2014
9222(2^220081+794)/266251Stefano Morozzi01/2020
92232^220044-9730566240Lelio R Paula04/2012
9224(77*10^66237-257)/966238Robert Price10/2017
922629^45285+266225Ray Chandler08/2011
9225(2^219993+1754)/266225Stefano Morozzi12/2019
922716711^9178+9178^1671166222Hans Havermann08/2019
9228(2^219928+462)/266205Stefano Morozzi12/2019
922915^56289+3866202Lelio R Paula08/2013
92303^138749+9866201Lelio R Paula06/2013
9231(21*2^219912-1)/566201Lelio R Paula01/2014
92332^219904-1699566198Lelio R Paula10/2011
92322^219903-461566198Yves Minet05/2019
9234(3^138712-2)/529766179Lelio R Paula04/2012
9235Phi(198552,10)66177Ray Chandler07/2010
92364*6^85041+766176Lelio R Paula09/2014
923716777^8794+8794^1677766172Hans Havermann08/2019
92382^219812-314966171Yves Minet10/2009
92392^219795-61116766165Paul Bourdelais03/2013
924032455!2+51266162Robert Price02/2015
9241(27*2^219760-1)/22766154Lelio R Paula01/2014
9243(11^63521-4^63521)/766150Robert Price03/2013
92425*7^78274-666150Lelio R Paula09/2014
924415853^14872+14872^1585366145Hans Havermann08/2019
9245(2^219706+1282)/266138Stefano Morozzi12/2019
9246(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
92472^219679-11201566130Enzo Doria05/2014
92482^219653+15015*21965366123Henri Lifchitz04/2005
9249(2^219621+2670)/266113Stefano Morozzi12/2019
925015445^15782-15782^1544566108Norbert Schneider08/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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